Problem: Simplify the following expression: $\dfrac{35p^3}{7p^2}$ You can assume $p \neq 0$.
Solution: $ \dfrac{35p^3}{7p^2} = \dfrac{35}{7} \cdot \dfrac{p^3}{p^2} $ To simplify $\frac{35}{7}$ , find the greatest common factor (GCD) of $35$ and $7$ $35 = 5 \cdot 7$ $7 = 7$ $ \mbox{GCD}(35, 7) = 7 $ $ \dfrac{35}{7} \cdot \dfrac{p^3}{p^2} = \dfrac{7 \cdot 5}{7 \cdot 1} \cdot \dfrac{p^3}{p^2} $ $\phantom{ \dfrac{35}{7} \cdot \dfrac{3}{2}} = 5 \cdot \dfrac{p^3}{p^2} $ $ \dfrac{p^3}{p^2} = \dfrac{p \cdot p \cdot p}{p \cdot p} = p $ $ 5 \cdot p = 5p $